立方晶体弹性常数和EAM/FS势函数的关系  

Relationships Between Elastic Constants and EAM/FS Potential Functions for Cubic Crystals

作　　者：段灵杰 刘永长[1] DUAN Lingjie;LIU Yongchang(State Key Lab of Hydraulic Engineering Simulation and Safety,School of Materials Science and Engineering,Tianjin University,Tianjin 300354,China)

机构地区：[1]天津大学材料科学与工程学院水利安全与仿真国家重点实验室

出　　处：《金属学报》2020年第1期112-118,共7页Acta Metallurgica Sinica

基　　金：国家自然科学基金项目No.U1660201;国家磁约束核聚变能源研究专项课题项目No.2015GB119001~~

摘　　要：为了确定bcc和fcc晶体的EAM/FS势函数参数,研究了EAM/FS势函数与弹性常数的关系。对bcc和fcc结构晶体,分别导出压强(P)和体积弹性模量(B)、弹性常数(C44)和剪切弹性模量(Cp=(C11-C12)/2)的利用嵌入函数、对势函数和电子密度分布函数的表达式。发现C44和Cp的大小不仅取决于所考虑的原子和周围原子的距离,还受近邻原子排列状况的影响。将关于结合能(utot)和P、B、C44、C)p的5个拟合方程转化为求最小值的优化模型,给出了5种典型bcc结构晶体(V、Mo、Nb、Ta、W)和3种典型fcc结构晶体(Cu、γ-Fe、Ni)的结合能中待定参数的值。采用上述参数计算得到的最小结合能与实验结果一致,此时所对应的原子间距与晶格常数相同,表明了方法的有效性。Potential functions are extensively applied in molecular dynamics(MD) simulation of metals. Selection of them is a very important step in MD simulations due to its effects of the precision and reliability of the simulations. They are one of the most important reference data during the process of calculation. In order to cover the shortage of pairwise potentials for modelling transition metals, EAM/FS manybody potentials have been introduced since 80’s of last century. For the sake of determining parameters in the EAM/FS potential functions of bcc and fcc crystals through macro mechanical properties, relations between the EAM/FS potential functions and elastic constants were investigated in this work. Expressions of the pressure(P) and the bulk modulus(B), elastic constant(C44) and shear elastic modulus(Cp=(C11-C12)/2) in terms of the embedding function, pair potential function and the electron density distribution function were deduced for bcc and fcc structures, respectively. It was found that the magnitude of the C44 and Cp depends on the distances between the considered atom and surrounding atoms, but also the configuration of surrounding atoms. Finally, by converting five fitting equations about the cohesive energy(utot) and P, B, C44, Cp into an optimization model of finding minimum value, the values of the six undeter-mined parameters in the cohesive energy were given for five typical bcc crystals(V, Mo, Nb, Ta and W)and three typical fcc crystals(Cu, γ-Fe, Ni), respectively. For each crystal, calculation errors show accuracy of parameter values. The obtained calculation results, for the minimum cohesive energy and the corresponding atomic distance, fit well with the reported experimental data, by adopting the above values of the parameters, which indicates the effectiveness for our method.

关 键 词：立方晶体 弹性常数 EAM势 FS势 

分 类 号：TG111.3[金属学及工艺—物理冶金] TG113.2[金属学及工艺—金属学]